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Journal of Applied Mathematics
Volume 2012, Article ID 383282, 19 pages
Research Article

Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems

1School of Mathematics and Statistics, Henan University of Science and Technology, Henan, Luoyang 471003, China
2College of Mathematics and Science, Luoyang Normal University, Henan, Luoyang 471022, China

Received 29 August 2011; Revised 14 January 2012; Accepted 27 January 2012

Academic Editor: Nicola Guglielmi

Copyright © 2012 Yusen Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The linearizability (or isochronicity) problem is one of the open problems for polynomial differential systems which is far to be solved in general. A progressive way to find necessary conditions for linearizability is to compute period constants. In this paper, we are interested in the linearizability problem of p : −q resonant degenerate singular point for polynomial differential systems. Firstly, we transform degenerate singular point into the origin via a homeomorphism. Moreover, we establish a new recursive algorithm to compute the so-called generalized period constants for the origin of the transformed system. Finally, to illustrate the effectiveness of our algorithm, we discuss the linearizability problems of 1 : −1 resonant degenerate singular point for a septic system. We stress that similar results are hardly seen in published literatures up till now. Our work is completely new and extends existing ones.